Subgroups — #18088642

Order 4864.

834 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926586	C₂	1	1	yes	maximal, characteristic
2	#14565991	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926312	C₂	1	1	yes	maximal, characteristic
4	#14563356	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926304	C₂	1	1	yes	maximal, characteristic
6	#14561865	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#339	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₂²	1	1	yes	characteristic
9	C₂×#10597372	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
12	#11926586	—	2	2	no	—
13	#11926586	C₄	1	4	yes	complemented
14	C₂×#10597275	—	2	1	no	—
15	C₂×#10597274	—	2	1	no	—
16	C₄⋊C₄×Dic₁₉	—	2	1	no	—
17	C₄⋊C₄×Dic₁₉	—	2	1	no	—
18	C₄×C₄⋊Dic₁₉	—	2	1	no	—
19	C₄×C₄⋊Dic₁₉	—	2	1	no	—
20	C₂²⋊C₄×Dic₁₉	—	2	2	no	—
21	C₂×C₁₉⋊#95	—	2	2	no	—
22	#11926312	C₄	1	4	yes	complemented
23	#11926306	—	2	1	no	—
24	#11926306	—	2	1	no	—
25	#11926304	—	2	2	no	—
26	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
29	C₁₉×#339	C₄	1	4	yes	complemented
30	C₂³×C₄×C₁₉	—	2	1	no	—
31	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
32	C₂³×Dic₁₉	—	2	1	no	—
33	C₂³×Dic₁₉	D₄	1	2	yes	—
34	C₂×M₁₆×C₁₉	—	2	1	no	—
35	C₂×M₁₆×C₁₉	—	2	1	no	—
36	C₂×M₁₆×C₁₉	—	2	1	no	—
37	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
38	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
39	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
40	C₂²×C₈×C₁₉	—	2	1	no	—
41	C₁₉×#117	—	2	1	no	—
42	C₁₉×#117	—	2	1	no	—
43	C₁₉×#117	C₂×C₄	1	2	yes	—
44	C₁₉×#117	Q₈	1	2	yes	—
45	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
46	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
47	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
48	C₂×C₄²×C₁₉	—	2	1	no	—
49	C₂×C₄²×C₁₉	—	2	1	no	—
50	C₂×C₄²×C₁₉	—	2	1	no	—
51	C₂×C₄²×C₁₉	—	2	1	no	—
52	C₂×C₄²×C₁₉	—	2	1	no	—
53	C₂×C₄²×C₁₉	—	2	1	no	—
54	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
55	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
56	#10597372	—	2	1	no	—
57	#10597372	—	2	1	no	—
58	#10597372	C₂×C₄	1	2	yes	—
59	#10597372	D₄	1	2	yes	—
60	C₂×C₄⋊Dic₁₉	—	2	1	no	—
61	C₂×C₄⋊Dic₁₉	—	2	1	no	—
62	C₂×C₄⋊Dic₁₉	—	2	1	no	—
63	C₂×C₄⋊Dic₁₉	—	2	1	no	—
64	C₂×C₄⋊Dic₁₉	—	2	1	no	—
65	C₂×C₄⋊Dic₁₉	—	2	1	no	—
66	C₂×C₄⋊Dic₁₉	—	2	1	no	—
67	C₂×C₄⋊Dic₁₉	—	2	1	no	—
68	C₂×C₄⋊Dic₁₉	—	2	1	no	—
69	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
70	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
71	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
72	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
73	C₂×C₄⋊Dic₁₉	Q₈	1	2	yes	—
74	C₂×C₄×Dic₁₉	—	2	1	no	—
75	C₂×C₄×Dic₁₉	—	2	2	no	—
76	C₂×C₄×Dic₁₉	—	2	2	no	—
77	C₂×#64520	—	2	1	no	—
78	C₂×#64520	—	2	1	no	—
79	C₂×#64520	—	2	1	no	—
80	C₂×#64520	—	2	1	no	—
81	C₂×#64520	—	2	1	no	—
82	C₂×#64520	C₂×C₄	1	2	yes	—
83	C₂²×C₁₉⋊C₈	—	2	1	no	—
84	C₁₉⋊#95	—	2	2	no	—
85	C₁₉⋊#95	—	2	2	no	—
86	C₁₉⋊#95	—	4	4	no	—
87	#10597275	—	2	4	no	—
88	#10597274	—	2	4	no	—
89	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	—	2	2	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	—	2	2	no	—
93	C₂²×C₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	—	2	1	no	—
95	C₂²×C₄×C₁₉	—	4	1	no	—
96	C₂²×C₄×C₁₉	—	4	1	no	—
97	C₂²×C₄×C₁₉	—	4	1	no	—
98	C₂²×C₄×C₁₉	—	4	1	no	—
99	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
113	C₂²×Dic₁₉	—	2	1	no	—
114	C₂²×Dic₁₉	—	2	1	no	—
115	C₂²×Dic₁₉	—	2	2	no	—
116	C₂²×Dic₁₉	—	2	2	no	—
117	C₂²×Dic₁₉	—	2	2	no	—
118	C₂²×Dic₁₉	—	4	2	no	—
119	C₂²×Dic₁₉	—	4	2	no	—
120	C₂²×Dic₁₉	—	4	2	no	—
121	C₂²×Dic₁₉	—	4	2	no	—
122	C₂²×Dic₁₉	—	4	1	no	—
123	C₂²×Dic₁₉	—	4	1	no	—
124	C₂²×Dic₁₉	C₄⋊C₄	1	4	yes	—
125	M₁₆×C₁₉	—	2	2	no	—
126	M₁₆×C₁₉	—	2	2	no	—
127	M₁₆×C₁₉	—	2	2	no	—
128	M₁₆×C₁₉	C₄²	1	4	yes	complemented
129	C₂×C₈×C₁₉	—	2	2	no	—
130	C₂×C₈×C₁₉	—	2	2	no	—
131	C₂×C₈×C₁₉	—	2	2	no	—
132	C₄⋊C₄×C₁₉	—	2	1	no	—
133	C₄⋊C₄×C₁₉	—	2	1	no	—
134	C₄⋊C₄×C₁₉	C₄⋊C₄	1	2	yes	—
135	C₄⋊C₄×C₁₉	C₄⋊C₄	1	2	yes	—
136	C₂²⋊C₄×C₁₉	—	2	2	no	—
137	C₂²⋊C₄×C₁₉	—	2	2	no	—
138	C₄²×C₁₉	—	2	2	no	—
139	C₄²×C₁₉	—	2	2	no	—
140	C₄²×C₁₉	—	2	2	no	—
141	C₄²×C₁₉	—	2	2	no	—
142	C₄²×C₁₉	—	4	1	no	—
143	C₄²×C₁₉	—	4	1	no	—
144	C₂²⋊Dic₁₉	—	2	2	no	—
145	C₂²⋊Dic₁₉	—	2	2	no	—
146	C₄⋊Dic₁₉	—	2	2	no	—
147	C₄⋊Dic₁₉	—	2	2	no	—
148	C₄⋊Dic₁₉	—	2	2	no	—
149	C₄⋊Dic₁₉	—	2	2	no	—
150	C₄⋊Dic₁₉	—	2	1	no	—
151	C₄⋊Dic₁₉	—	2	1	no	—
152	C₄⋊Dic₁₉	—	2	2	no	—
153	C₄⋊Dic₁₉	—	2	2	no	—
154	C₄⋊Dic₁₉	—	4	1	no	—
155	C₄⋊Dic₁₉	—	4	1	no	—
156	C₄⋊Dic₁₉	C₂²⋊C₄	1	2	yes	—
157	C₄⋊Dic₁₉	C₂²⋊C₄	1	2	yes	—
158	C₄×Dic₁₉	—	2	2	no	—
159	C₄×Dic₁₉	—	2	2	no	—
160	C₄×Dic₁₉	—	8	2	no	—
161	C₄×Dic₁₉	—	8	2	no	—
162	#64520	—	2	2	no	—
163	#64520	—	2	2	no	—
164	#64520	—	4	1	no	—
165	#64520	—	4	1	no	—
166	C₂×C₁₉⋊C₈	—	2	2	no	—
167	C₂×C₁₉⋊C₈	—	4	1	no	—
168	C₂×C₁₉⋊C₈	—	4	1	no	—
169	#10899	—	19	1	no	maximal, Sylow
170	C₂³×C₁₉	—	2	1	no	—
171	C₂³×C₁₉	—	2	1	no	—
172	C₂³×C₁₉	—	2	1	no	—
173	C₂³×C₁₉	—	2	1	no	—
174	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
176	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
177	C₂³×C₁₉	#120	1	1	yes	characteristic
178	C₂³×C₁₉	#121	1	1	yes	characteristic
179	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
180	C₂³×C₁₉	#123	1	1	yes	characteristic
181	C₂×C₄×C₁₉	—	2	4	no	—
182	C₂×C₄×C₁₉	—	2	2	no	—
183	C₂×C₄×C₁₉	—	2	2	no	—
184	C₂×C₄×C₁₉	—	4	2	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	1	no	—
191	C₂×C₄×C₁₉	—	4	1	no	—
192	C₂×C₄×C₁₉	—	4	1	no	—
193	C₂×C₄×C₁₉	—	4	1	no	—
194	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
197	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
198	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
199	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
203	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
204	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
207	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
208	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
209	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
210	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
211	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
212	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
213	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
214	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
215	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
216	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
217	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
218	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
219	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
220	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
221	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
222	C₂×Dic₁₉	—	2	4	no	—
223	C₂×Dic₁₉	—	2	2	no	—
224	C₂×Dic₁₉	—	2	2	no	—
225	C₂×Dic₁₉	—	4	1	no	—
226	C₂×Dic₁₉	—	4	2	no	—
227	C₂×Dic₁₉	—	4	1	no	—
228	C₂×Dic₁₉	—	4	1	no	—
229	C₂×Dic₁₉	—	4	2	no	—
230	C₂×Dic₁₉	—	4	1	no	—
231	C₂×Dic₁₉	—	4	4	no	—
232	C₂×Dic₁₉	—	4	4	no	—
233	C₂×Dic₁₉	—	4	2	no	—
234	C₂×Dic₁₉	—	8	2	no	—
235	C₂×Dic₁₉	—	8	2	no	—
236	C₂×Dic₁₉	—	8	1	no	—
237	C₂×Dic₁₉	—	8	1	no	—
238	C₈×C₁₉	—	2	4	no	—
239	C₁₉⋊C₈	—	4	2	no	—
240	C₂×#428	—	19	1	no	—
241	#2274	—	19	1	no	—
242	C₂×#343	—	19	1	no	—
243	#1736	—	19	1	no	—
244	C₂×#339	—	19	1	no	—
245	C₂×#339	D₁₉	1	1	yes	characteristic
246	C₄⋊#95	—	19	1	no	—
247	C₂²×C₁₉	—	2	1	no	—
248	C₂²×C₁₉	—	2	1	no	—
249	C₂²×C₁₉	—	2	1	no	—
250	C₂²×C₁₉	—	2	1	no	—
251	C₂²×C₁₉	—	2	1	no	—
252	C₂²×C₁₉	—	2	1	no	—
253	C₂²×C₁₉	—	2	1	no	—
254	C₂²×C₁₉	—	2	1	no	—
255	C₂²×C₁₉	—	2	1	no	—
256	C₂²×C₁₉	—	2	1	no	—
257	C₂²×C₁₉	—	2	1	no	—
258	C₂²×C₁₉	—	2	1	no	—
259	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
260	C₂²×C₁₉	#385	1	1	yes	characteristic
261	C₂²×C₁₉	#385	1	1	yes	characteristic
262	C₂²×C₁₉	#386	1	1	yes	characteristic
263	C₂²×C₁₉	#387	1	1	yes	characteristic
264	C₂²×C₁₉	#388	1	1	yes	characteristic
265	C₂²×C₁₉	#389	1	1	yes	characteristic
266	C₂²×C₁₉	#453	1	1	yes	characteristic
267	C₂²×C₁₉	#454	1	1	yes	characteristic
268	C₂²×C₁₉	#455	1	1	yes	characteristic
269	C₂²×C₁₉	#456	1	1	yes	characteristic
270	C₄×C₁₉	—	4	4	no	—
271	C₄×C₁₉	—	4	2	no	—
272	C₄×C₁₉	—	4	2	no	—
273	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
274	C₄×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
275	C₄×C₁₉	#387	1	1	yes	characteristic
276	C₄×C₁₉	#387	1	1	yes	characteristic
277	C₄×C₁₉	#387	1	1	yes	characteristic
278	C₄×C₁₉	#388	1	1	yes	characteristic
279	C₄×C₁₉	#389	1	1	yes	characteristic
280	C₄×C₁₉	#391	1	1	yes	characteristic
281	Dic₁₉	—	4	4	no	—
282	Dic₁₉	—	4	2	no	—
283	Dic₁₉	—	4	2	no	—
284	Dic₁₉	—	8	2	no	—
285	C₂²×M₁₆	—	19	1	no	—
286	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
287	C₂×#117	—	19	1	no	—
288	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
289	C₂²×C₄⋊C₄	—	19	1	no	—
290	C₂²×C₄⋊C₄	—	19	1	no	—
291	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
292	#428	—	19	4	no	—
293	#428	—	38	2	no	—
294	C₂×#107	—	38	1	no	—
295	C₂×#106	—	38	1	no	—
296	C₄×C₄⋊C₄	—	38	1	no	—
297	C₄×C₄⋊C₄	—	38	1	no	—
298	C₄×C₄⋊C₄	—	38	1	no	—
299	C₄×C₄⋊C₄	—	38	1	no	—
300	C₄×C₂²⋊C₄	—	38	2	no	—
301	C₂×#95	—	38	2	no	—
302	#343	—	19	4	no	—
303	#340	—	38	1	no	—
304	#340	—	38	1	no	—
305	#339	—	38	2	no	—
306	#339	Dic₁₉	1	4	yes	complemented
307	C₂×C₁₉	—	2	1	no	—
308	C₂×C₁₉	—	2	1	no	—
309	C₂×C₁₉	—	2	1	no	—
310	C₂×C₁₉	—	2	1	no	—
311	C₂×C₁₉	#1436	1	1	yes	characteristic
312	C₂×C₁₉	#1856	1	1	yes	characteristic
313	C₂×C₁₉	#1857	1	1	yes	characteristic
314	C₂×C₁₉	#1859	1	1	yes	characteristic
315	C₂×C₁₉	#1860	1	1	yes	characteristic
316	C₂×C₁₉	#1882	1	1	yes	characteristic
317	C₂×C₁₉	#1883	1	1	yes	characteristic
318	C₂³×C₄	—	2	1	no	—
319	C₂³×C₄	—	19	2	no	—
320	C₂³×C₄	—	38	1	no	—
321	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
322	C₂×M₁₆	—	2	1	no	—
323	C₂×M₁₆	—	2	1	no	—
324	C₂×M₁₆	—	2	1	no	—
325	C₂×M₁₆	—	19	2	no	—
326	C₂×M₁₆	—	38	1	no	—
327	C₂×M₁₆	—	38	1	no	—
328	C₂×M₁₆	—	38	1	no	—
329	C₂×M₁₆	—	38	1	no	—
330	C₂×M₁₆	—	38	1	no	—
331	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
332	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
333	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	—
334	C₂²×C₈	—	2	1	no	—
335	C₂²×C₈	—	38	1	no	—
336	#117	—	2	1	no	—
337	#117	—	2	1	no	—
338	#117	—	19	2	no	—
339	#117	—	19	2	no	—
340	#117	—	38	1	no	—
341	#117	—	38	1	no	—
342	#117	Dic₃₈	1	2	yes	—
343	#117	C₂×Dic₁₉	1	2	yes	—
344	C₂×C₄⋊C₄	—	19	1	no	—
345	C₂×C₄⋊C₄	—	19	1	no	—
346	C₂×C₄⋊C₄	—	19	2	no	—
347	C₂×C₄⋊C₄	—	19	2	no	—
348	C₂×C₄⋊C₄	—	19	2	no	—
349	C₂×C₄⋊C₄	—	38	1	no	—
350	C₂×C₄⋊C₄	—	38	1	no	—
351	C₂×C₄⋊C₄	—	38	1	no	—
352	C₂×C₄⋊C₄	—	38	1	no	—
353	C₂×C₄⋊C₄	—	38	1	no	—
354	C₂×C₄⋊C₄	—	38	1	no	—
355	C₂×C₄⋊C₄	—	38	1	no	—
356	C₂×C₄⋊C₄	—	38	1	no	—
357	C₂×C₄⋊C₄	—	38	1	no	—
358	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
359	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
360	C₂×C₂²⋊C₄	—	2	1	no	—
361	C₂×C₂²⋊C₄	—	38	1	no	—
362	C₂×C₄²	—	2	1	no	—
363	C₂×C₄²	—	2	1	no	—
364	C₂×C₄²	—	2	1	no	—
365	C₂×C₄²	—	2	1	no	—
366	C₂×C₄²	—	2	1	no	—
367	C₂×C₄²	—	2	1	no	—
368	C₂×C₄²	—	38	1	no	—
369	C₂×C₄²	—	38	2	no	—
370	C₂×C₄²	—	38	2	no	—
371	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
372	#107	—	38	4	no	—
373	#106	—	38	4	no	—
374	#95	—	38	2	no	—
375	#95	—	38	2	no	—
376	#95	—	76	4	no	—
377	C₁₉	#10899	1	1	yes	characteristic, complemented, Sylow
378	C₂⁴	D₄×D₁₉	1	1	yes	characteristic
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	4	1	no	—
385	C₂²×C₄	—	4	1	no	—
386	C₂²×C₄	—	4	1	no	—
387	C₂²×C₄	—	4	1	no	—
388	C₂²×C₄	—	19	4	no	—
389	C₂²×C₄	—	38	1	no	—
390	C₂²×C₄	—	38	1	no	—
391	C₂²×C₄	—	38	2	no	—
392	C₂²×C₄	—	38	2	no	—
393	C₂²×C₄	—	38	2	no	—
394	C₂²×C₄	—	76	2	no	—
395	C₂²×C₄	—	76	2	no	—
396	C₂²×C₄	—	76	2	no	—
397	C₂²×C₄	—	76	2	no	—
398	C₂²×C₄	—	76	1	no	—
399	C₂²×C₄	—	76	1	no	—
400	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
401	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
402	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
404	C₂²×C₄	#64541	1	1	yes	characteristic
405	C₂²×C₄	#64541	1	1	yes	characteristic
406	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
407	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
408	C₂²×C₄	#64543	1	1	yes	characteristic
409	C₂²×C₄	#64543	1	1	yes	characteristic
410	C₂²×C₄	#64543	1	1	yes	characteristic
411	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
412	C₂²×C₄	#64545	1	1	yes	characteristic
413	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
414	M₁₆	—	2	2	no	—
415	M₁₆	—	2	2	no	—
416	M₁₆	—	2	2	no	—
417	M₁₆	—	38	2	no	—
418	M₁₆	—	38	2	no	—
419	M₁₆	—	76	1	no	—
420	M₁₆	—	76	1	no	—
421	M₁₆	C₄×Dic₁₉	1	4	yes	complemented
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	38	2	no	—
426	C₂×C₈	—	76	1	no	—
427	C₂×C₈	—	76	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	19	2	no	—
431	C₄⋊C₄	—	19	2	no	—
432	C₄⋊C₄	—	38	2	no	—
433	C₄⋊C₄	—	38	2	no	—
434	C₄⋊C₄	—	38	1	no	—
435	C₄⋊C₄	—	38	1	no	—
436	C₄⋊C₄	—	38	2	no	—
437	C₄⋊C₄	—	38	2	no	—
438	C₄⋊C₄	—	38	2	no	—
439	C₄⋊C₄	—	38	2	no	—
440	C₄⋊C₄	—	76	1	no	—
441	C₄⋊C₄	—	76	1	no	—
442	C₄⋊C₄	C₄⋊Dic₁₉	1	2	yes	—
443	C₄⋊C₄	C₄⋊Dic₁₉	1	2	yes	—
444	C₂²⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	—	38	2	no	—
447	C₂²⋊C₄	—	38	2	no	—
448	C₄²	—	2	2	no	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	2	no	—
451	C₄²	—	2	2	no	—
452	C₄²	—	4	1	no	—
453	C₄²	—	4	1	no	—
454	C₄²	—	38	2	no	—
455	C₄²	—	38	2	no	—
456	C₄²	—	152	2	no	—
457	C₄²	—	152	2	no	—
458	C₂³	—	2	1	no	—
459	C₂³	—	2	1	no	—
460	C₂³	—	2	1	no	—
461	C₂³	—	2	1	no	—
462	C₂³	#10597324	1	1	yes	characteristic
463	C₂³	#10597328	1	1	yes	characteristic
464	C₂³	#10597329	1	1	yes	characteristic
465	C₂³	#10597330	1	1	yes	characteristic
466	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
467	C₂³	#10597339	1	1	yes	characteristic
468	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	38	4	no	—
483	C₂×C₄	—	38	2	no	—
484	C₂×C₄	—	38	2	no	—
485	C₂×C₄	—	76	1	no	—
486	C₂×C₄	—	76	2	no	—
487	C₂×C₄	—	76	1	no	—
488	C₂×C₄	—	76	1	no	—
489	C₂×C₄	—	76	2	no	—
490	C₂×C₄	—	76	1	no	—
491	C₂×C₄	—	76	4	no	—
492	C₂×C₄	—	76	4	no	—
493	C₂×C₄	—	76	2	no	—
494	C₂×C₄	—	152	2	no	—
495	C₂×C₄	—	152	2	no	—
496	C₂×C₄	—	152	1	no	—
497	C₂×C₄	—	152	1	no	—
498	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
499	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
500	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
501	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
502	C₂×C₄	#10597323	1	1	yes	characteristic
503	C₂×C₄	#10597324	1	1	yes	characteristic
504	C₂×C₄	#10597325	1	1	yes	characteristic
505	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
506	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
507	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
508	C₂×C₄	#10597331	1	1	yes	characteristic
509	C₂×C₄	#10597332	1	1	yes	characteristic
510	C₂×C₄	#10597333	1	1	yes	characteristic
511	C₂×C₄	#10597334	1	1	yes	characteristic
512	C₂×C₄	#10597335	1	1	yes	characteristic
513	C₂×C₄	#10597336	1	1	yes	characteristic
514	C₂×C₄	#10597338	1	1	yes	characteristic
515	C₂×C₄	#10597340	1	1	yes	characteristic
516	C₂×C₄	#10597341	1	1	yes	characteristic
517	C₂×C₄	#10597342	1	1	yes	characteristic
518	C₂×C₄	#10597343	1	1	yes	characteristic
519	C₂×C₄	#10597344	1	1	yes	characteristic
520	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
521	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
522	C₂×C₄	#10597372	1	1	yes	characteristic
523	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
524	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
525	C₂×C₄	Q₈×Dic₁₉	1	1	yes	characteristic
526	C₈	—	2	4	no	—
527	C₈	—	76	2	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	1	no	—
533	C₂²	—	2	1	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	2	1	no	—
540	C₂²	C₄⋊C₄×Dic₁₉	1	1	yes	characteristic
541	C₂²	#11926418	1	1	yes	characteristic
542	C₂²	#11926419	1	1	yes	characteristic
543	C₂²	#11926422	1	1	yes	characteristic
544	C₂²	#11926427	1	1	yes	characteristic
545	C₂²	#11926437	1	1	yes	characteristic
546	C₂²	#11926441	1	1	yes	characteristic
547	C₂²	#11926713	1	1	yes	characteristic
548	C₂²	#11926718	1	1	yes	characteristic
549	C₂²	#11926723	1	1	yes	characteristic
550	C₂²	#11926728	1	1	yes	characteristic
551	C₄	—	4	4	no	—
552	C₄	—	4	2	no	—
553	C₄	—	4	2	no	—
554	C₄	—	76	4	no	—
555	C₄	—	76	2	no	—
556	C₄	—	76	2	no	—
557	C₄	—	152	2	no	—
558	C₄	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
559	C₄	C₄×C₄⋊Dic₁₉	1	1	yes	characteristic
560	C₄	#11926429	1	1	yes	characteristic
561	C₄	#11926430	1	1	yes	characteristic
562	C₄	#11926431	1	1	yes	characteristic
563	C₄	#11926436	1	1	yes	characteristic
564	C₄	#11926443	1	1	yes	characteristic
565	C₄	#11926448	1	1	yes	characteristic
566	C₂	—	2	1	no	—
567	C₂	—	2	1	no	—
568	C₂	—	2	1	no	—
569	C₂	—	2	1	no	—
570	C₂	#14561869	1	1	yes	characteristic
571	C₂	#14563846	1	1	yes	characteristic
572	C₂	#14563851	1	1	yes	characteristic
573	C₂	#14563863	1	1	yes	characteristic
574	C₂	#14563870	1	1	yes	characteristic
575	C₂	#14564005	1	1	yes	characteristic
576	C₂	#14564012	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597328
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#339	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#339	D₁₉
hypocenter	C₁₉	#10899
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#339

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
13. #11926586	C₄	semidirect
22. #11926312	C₄	semidirect
29. C₁₉×#339	C₄	semidirect
128. M₁₆×C₁₉	C₄²	semidirect
306. #339	Dic₁₉	semidirect
377. C₁₉	#10899	semidirect
421. M₁₆	C₄×Dic₁₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#11926586	2
#14565991	2
C₂×#11926312	2
#14563356	2
C₂×#11926304	2
#14561865	2
C₂×C₁₉×#339	2
#10899	19